Yes, initializing the key during pairing would work great.
I posted my reply before the parent's edit. I don't think this is an intractable problem; my suggestion of a physical connection for pairing or even a remote pairing with a button press would work fine. My ONLY point was that hard coding a symmetric key into the keyboard/dongle pair and then using that key for all communication wouldn't be practical.
I posted my reply before the parent's edit. I don't think this is an intractable problem; my suggestion of a physical connection for pairing or even a remote pairing with a button press would work fine. My ONLY point was that hard coding a symmetric key into the keyboard/dongle pair and then using that key for all communication wouldn't be practical.